Ok, so I did a lot of reading and playing. Love those Pi's...however in this case I tried it on my new Pi Zero W and got...Segmentation fault. Ugh. After much more research I find out that both the original Pi Zero and the latest Pi Zero W use the same ARMv6 architecture and the dotNet Core runtime uses instruction sets from ARMv7 architecture. So I need to plug in my Rpi3B (64bitARMv8) which will run it splendidly.
Also interestingly, there is no build process available on the RPi (yet) so you cross-build the binaries under Windows CLI and then SFTP it over to the RPi to run. Rather easy, actually. I used the following websites for info in case anyone else is interested:
1. install for Windows: //www.microsoft.com/net/core/preview#windowscmd
2. manually install the ubuntu pre-reqs on your Raspian distro RPi: //github.com/dotnet/core/blob/master/Documentation/prereqs.md
3. create a few config files in your Windows install: //github.com/dotnet/core/blob/master/samples/RaspberryPiInstructions.md
4. do the helloworld app and SFTP it over to your RPi and run it. Yay!
For the AMR client it looks like I will need to wait for the stand-alone program to be separated from the runtime binaries before I can run it on my RPi, but at least I'm all ready now.